This article shows how to allow your user to delete an article if it is greyed out.
When you go to More -> Delete it will be greyed out like the following:
The ability to delete is only accessible to the Editor Role or higher. In order to change your role have your Admin go into the Control Panel and modify the role for your user to Editor. If the admin needs help with this, point them at the user management article where they can change the role under seat management.